Electro Magnetic Induction And Alternating Currents Question 143
Question: Match the following Currents r.m.s. values (1) $ x_{0}\sin \omega ,t $ (i) x0 (2) $ x_{0}\sin \omega ,t\cos \omega ,t $ (ii) $ \frac{x_{0}}{\sqrt{2}} $ (3) $ x_{0}\sin \omega ,t+x_{0}\cos \omega ,t $ (iii) $ \frac{x_{0}}{(2\sqrt{2})} $
Options:
A) 1. (i), 2. (ii), 3. (iii)
B) 1. (ii), 2. (iii), 3. (i)
C) 1. (i), 2. (iii), 3. (ii)
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
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rms value = $ \frac{x_{0}}{\sqrt{2}} $
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$ x_{0}\sin \omega t\cos \omega t=\frac{x_{0}}{2}\sin 2\omega t\Rightarrow rms\ value =\frac{x_{0}}{2\sqrt{2}} $
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$ x_{0}\sin \omega t+x_{0}\cos \omega t\Rightarrow rms\ value = \sqrt{{{( \frac{x_{0}}{\sqrt{2}} )}^{2}}+{{( \frac{x_{0}}{\sqrt{2}} )}^{2}}} $ $ =\sqrt{x_{0}^{2}}=x_{0} $
